In fact, the GRB neutrinos are emitted from long distant sources, and speed variation may be caused by different reasons [1]}. The in vacuo dispersion due to Lorentz invariance violation is one of the probable options, as well as the cosmic matter effect. Therefore, the time difference between neutrino observed time and the GRB trigger time may be days or even months, depending on the neutrino energy with the assumption of a sizable Lorentz violation of neutrinos. On the other hand, ultra-high energy neutrinos can be distinguished from neutrinos produced in the atmosphere and other backgrounds.
No matter from the theoretical analyses [1]}, [3]}, [4]}, [5]} or the IceCube measurements [6]}, [7]}, [8]}, [9]}, [10]}, ultra-high energy neutrinos above 60 TeV can stand out from backgrounds, thus render our analysis on the limit of GRB neutrino flux more convincing.
